I drove the Stelvio Pass on my last trip to Europe. I only drove on it from Switzerland to Italy, i.e Downhill. We drove it at night time, and the turns were seriously tight!! I'd say uphill is the safer option, cos u find yourself carrying a lot of speed on the way down. In the first few bends I found myself underestimating the sheer angle and sharpness of the road!

IF your mate has the time, do it both ways, seeing as the border is still quite far after it.
It is undoubtably great fun! Just watch out for some Italian nutters racing up n down it, trying to beat there best time!